# Math Help - Vector Real Life Application

1. ## Vector Real Life Application

So, I can't solve this problem, I've tried for about 30 minutes...
I'm trying to set up a right triangle with the vectors and using the tip to tail method, but I'm not getting anywhere. Could anyone try to do the problem and explain it? Thanks.

Without the wind, a plane would fly due east at a rate of 150 mph. The wind is blowing southeast at a rate of 50 mph. The wind is blowing at a 45° angle from due east. How far off of the due east path does the wind blow the plane?

2. ## Re: Vector Real Life Application

Originally Posted by glambeth
So, I can't solve this problem, I've tried for about 30 minutes...
I'm trying to set up a right triangle with the vectors and using the tip to tail method, but I'm not getting anywhere. Could anyone try to do the problem and explain it? Thanks.

Without the wind, a plane would fly due east at a rate of 150 mph. The wind is blowing southeast at a rate of 50 mph. The wind is blowing at a 45° angle from due east. How far off of the due east path does the wind blow the plane?
Set up a triangle. Draw one side of length 150 to the right ("due east") representing the motion of the airplane. From the tip of that, draw a second side, 45 degrees down, of length 50, representing the wind. Finally connect to two ends to get the third side of the triangle, representing the actual path of the airplane.

You should be able to see that the "interior angle" of the triangle, at the point where the two first sides connect, is 180- 45= 135 degrees. You have a triangle with angle 145 degrees and adjacent sides of lengths 150 and 50. (That is not a "right triangle".)

Use the "cosine law": $c^2= a^2+ b^2- 2ab cos(C)$ where a, b, and c are the lengths of the three sides and C is the angle opposite c- i.e. between a and b so that "c" is the length of the actual path of the airplane.

Once you know that length you can use the sine law, $\frac{sin(B)}{b}= \frac{sin(C)}{c}$, to calculate angle "B", opposite side b, the side that was representing the wind. That is the angle "off east" that the problem is asking for.

3. ## Re: Vector Real Life Application

so c = 188.6979, C = 135, then would b = 50 or 150?